A salon and a cafe, 1500 m apart, are situated between Erika's house and Pamela's house. The cafe is halfway between the two houses and the salon is closer to Pamela's house. Erika and Pamela left their homes at the same time and arrived at the salon at the same time. Erika drove at a speed of 70 km/h while Pamela drove at a speed 10 km/h slower than Erika. Leaving your answer in kilometres,

1. how much farther did Erika travel than Pamela?
2. how far is Pamela's house from the cafe?

(a)
Let the distance between Erika's house and Pamela's house be 1 d.
Pamela travelled = ¹₂ d - 1500 m
Erika travelled = ¹₂ d + 1500 m

Distance that Erika travelled more than Pamela
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Erika took to travel to the salon
= 3 ÷ 10
= ³₁₀ h

Distance that Erika travelled
= ³₁₀ x 70
= 21 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Pamela's house and the cafe
= 21 - 1.5
= 19.5 km

Answer(s): (a) 3 km; (b) 19.5 km